Answers
x=18
Radius=√(7²+9²)=√130
(2*√130)²=x²+14²==>x²=√324=18
Related Questions
what is the product? (9t-4)(-9-4)
Answers
Answer: The product of [tex](9t-4)(-9-4)[/tex] is -117t+52.
Explanation:
The given expression is,
[tex](9t-4)(-9-4)[/tex]
Simplify the above expression.
[tex](9t-4)(-13)[/tex]
Use distributive property t simplify the above expression.
[tex](9t-4)(-13)=9t\times (-13)-4\times(-13)[/tex]
[tex](9t-4)(-13)=117t+52[/tex]
Therefore, the product of [tex](9t-4)(-9-4)[/tex] is -117t+52.
Find the area of a parallelogram with a height 15 cm and a base of 18 and 2/3 cm
Answers
The formula for area of a parallelogram is [tex]A = bh[/tex], where [tex]b[/tex] is the base and [tex]h[/tex] is the height.
You're given the values of both the base and the height, so you can just plug these values into the formula for area. It will be easier to multiply if we convert the mixed number to an improper fraction first, so I'll do that.
[tex]18 \frac{2}{3} = \frac{56}{3} [/tex]
[tex]A = bh[/tex]
[tex]A = \frac{56}{3} *15[/tex]
[tex]A= \frac{56}{3} * \frac{15}{1} [/tex]
[tex]A= \frac{840}{3} [/tex]
[tex]A=280[/tex]
Answer:
The area of the parallelogram is 280 cm².
A man 50 years old has 8 sons born of equal intervals. The sum of the ages of the father and sons is 186. What is the age of the eldest son if the youngest is 3 years old.,
Answers
To find the age of the eldest son in a family where the father is 50 and has 8 sons with a total age sum of 186, and the youngest son is 3, one can determine the age difference between siblings and use the formula for the sum of an arithmetic series.
The question is asking us to determine the age of the eldest son, given that the sum of the ages of a 50-year-old father and his 8 sons is 186 years and the youngest son is 3 years old. Let's assume that the sons are born at equal intervals; we can denote the age difference between each son as 'd' years.
The sequence of the sons' ages forms an arithmetic series where the youngest son is 3 years old (the first term of the series, or 'a1'), and the eldest son's age will be 'a1 + 7d' (since there are 8 sons).
Since the sum of an arithmetic series is given by the formula 'n/2 * (a1 + an)', where 'n' is the number of terms, 'a1' is the first term and 'an' is the last term, we can set up the equation:
8/2 * (3 + (3 + 7d)) = 186 - 50 (subtract the father's age from the total sum).
This simplifies to 4 * (3 + 3 + 7d) = 136, or '4 * (6 + 7d) = 136'. Dividing both sides by 4, we get '6 + 7d = 34', which leads to '7d = 28' and thus 'd = 4'.
Therefore, the age of the eldest son will be '3 + 7*4', which equals 31 years old.
Arrange the summation expressions in increasing order of their values.
Answers
[tex]\sum_{i=1}^{4}4(5)^{i-1} = (4(5)^{1-1}) + (4(5)^{2-1}) + (4(5)^{3-1}) + (4(5)^{4-1})[/tex]
[tex]=4+20+100+500 = 624 [/tex]
[tex]\sum_{i=1}^{5}3(4)^{i-1} = (3(4)^{1-1}) + (3(4)^{2-1}) + (3(4)^{3-1}) + (3(4)^{4-1}) + (3(4)^{5-1})[/tex]
[tex]=3+12+48+192+768=1023[/tex]
[tex]\sum_{i=1}^{2}5(6)^{i-1} = (5(6)^{1-1}) + (5(6)^{2-1})[/tex]
[tex]=5+30=35[/tex]
[tex]\sum_{i=1}^{4}5^{i-1} = (5^{1-1})+(5^{2-1})+(5^{3-1})+(5^{4-1}) [/tex]
[tex]=1 + 5+ 25+125 = 156[/tex]
So, our totals are: 624, 1023, 35, and 156. So clearly, 1023 > 624 > 156 > 35. W can write it as (your answer):
[tex]\sum_{i=1}^{2}5(6)^{i-1} <\sum_{i=1}^{4}5^{i-1} <\sum_{i=1}^{4}4(5)^{i-1} < \sum_{i=1}^{5}3(4)^{i-1} [/tex]
Hope this helps! If anything is confusing, you can always DM me.
∑ 4 * 5^(i-1) = 4 + 20 + 100 + 500 = 624
∑ 3 * 4^(i-1) = 3 + 12 + 48 + 192 + 768 = 1,023
∑ 5* 6^(i-1) = 5 + 30 = 35
∑ 5^(i-1) = 1 + 5 + 25 + 125 = 156
Answer:
∑ (i=1, 2) 5 * 6^(i-1) < ∑ (i=1, 4) 5^(i-1) < ∑ (i=1, 4) 4 * 5^(i-1) <
< ∑ (i=1, 5) 3 * 4^(i-1)
The sum of two numbers is 240. the larger number is 6 less than twice the smaller. find the numbers. the smaller number is , and the larger number is
Answers
----------
Let the smaller be "x" ; Larger is "2x-6"
EQUATION:
x + 2x-6 = 240
3x= 246
x = 82 (smaller)
2x-6 = 158 (larger)
The smaller number is 82 and the larger number is 158.
Given that, the sum of two numbers is 240.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the smaller number be x.
The larger number is 6 less than twice the smaller.
Larger number = 2x - 6
Now, the sum of two numbers is 240.
So, x+2x-6 = 240
⇒ 3x - 6 =240
⇒ 3x = 246
⇒ x = 82
Larger number = 240 - 82
= 158
Therefore, the smaller number is 82 and the larger number is 158.
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100p for an answer please
Answers
For n=5.3
5.3+8=13.3
All that apply:
1) First, write an expression.
2) the correct expression is: n + 8
3) second, substitute 5.3 for the variable, n.
4) third, simplify by adding 5.3 and 8
5) the answer is 13.3
A baker has three banana muffin recipes. Recipe A uses 3 bananas to make 12 muffins. Recipe Buses 5 bananas to make 24 muffins. Recipe C uses 11 bananas to make 48 muffins.
Answers
Answer:
From least to Greatest: B, C, A
Step-by-step explanation:
For each recipe, dividing the number of bananas needed by the number of muffins will give us the number of bananas per muffin.
A: 3/12 = 0.25B: 5/24 = 0.21C: 11/24 = 0.23As you can see here, Recipe A gives you 0.25 Bananas per muffin, Recipe B gives you 0.21 Bananas per muffin and recipe C will give you 0.23 Bananas per muffin.
Hope this helps!
Answer:
B,C,A
Step-by-step explanation:
54 is 60% of what number?
Enter your answer in the box.
Answers
I hope I helped!
Answer:The answer would be 90
Step-by-step explanation:
I would like help with the question. It's part of my assigment, but I have trouble with this type of math. If someone understands, can you explain it to me as well? For future reference?
In Panama City in January, high tide was at midnight. The water level at high tide was 9 feet and 1 foot at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in January for Panama City as a function of time (t).,
Answers
Problems where sine or cosine functions are used to model periodic behavior are problems in scaling. You need to match the period and amplitude of your scaled cosine function to the period and amplitude of the phenomenon you are modeling.
Here, high tides are 12 hours apart, so we need to scale x by a factor that turns 12 hours into 2π. That might be x ⇒ 2πx/12 or (π/6)x.
The high tide is 9 ft, and the low tide is 1 ft, so we need to do vertical offset and scaling to make the peak of our transformed cosine function be 9 and its minimum be 1. That difference is 8, so has an amplitude of ±4 around a midline of (9+1)/2 = 5.
Then our tide model is
.. water level = 5 +4*cos((π/6)t)
Find the volume of a cylinder with a radius of 5 cm and a height of 10 cm. Then, find the volume of the cylinder if the radius is increased to 10 cm. Leave your answers in term of pi.
Answers
[tex]v= \pi r^{2} h[/tex]
where v = volume of cylinder, r = radius, and h = height of cylinder.
1) Radius = 5 cm, height = 10 cm. Plug these values into the equation.
[tex]v= \pi 5^{2} (10) = 250 \pi [/tex]
2) Radius = 10 cm, height = 10 cm.
[tex]v= \pi 10^{2} (10) = 1000 \pi[/tex]
Volume of cylinder is 250πcm³ and volume of the new cylinder is 1000πcm³.
How to determine the volume of the cylinder?The volume of the cylinder can be determined by multiplying area of base with height of the cylinder.
V=πr²*h
where r is the radius of base of the cylinder and h is the height of the cylinder.
following this above formula in given problem,
radius of the base of the cylinder= 5cm
height of the cylinder=10cm
volume= V=πr²*h= π5²*10= 250π cm³
Now the radius of the cylinder is increased to 10cm.
now r=10cm
height of the cylinder=10cm
volume= V=πr²*h= π10²*10= 1000π cm³
Therefore volume of cylinder is 250πcm³ and volume of the new cylinder is 1000πcm³.
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Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°–45°–90° triangle) Prove: In a 45°–45°–90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this isosceles triangle becomes a2 + a2 = c2. By combining like terms, 2a2 = c2. Which final step will prove that the length of the hypotenuse, c, is times the length of each leg? Substitute values for a and c into the original Pythagorean theorem equation. Divide both sides of the equation by two, then determine the principal square root of both sides of the equation. Determine the principal square root of both sides of the equation. Divide both sides of the equation by 2.
Answers
2a^2= c^2
If we have square root
√2a^2=√c^2
a√2= c
Answer:
Step-by-step explanation:
In a 45°–45°–90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem that is:
[tex]a^{2}+b^{2}=c^{2}[/tex], which in this isosceles triangle becomes [tex]a^{2}+a^{2}=c^{2}[/tex] as a=b in isosceles triangle.
By combining the like terms, [tex]2a^{2}=c^{2}[/tex]
Now, we will determine the principal square root of both sides of the equation,
[tex]c=\sqrt{2}a[/tex] (since a is positive)
Divide both sides of the equation by 2, we get
[tex]\frac{c}{2}=\frac{\sqrt{2}a}{2}[/tex]
[tex]\frac{c}{2}=\frac{a}{\sqrt{2}}[/tex]
[tex]c=\frac{2a}{\sqrt{2}}[/tex]
[tex]c=\sqrt{2}a[/tex]
Now, as a=b, then [tex]c=\sqrt{2}b[/tex]
What is the area of a regular hexagon with a side length of 4 m? Enter your answer in the box. Round only your final answer to the nearest hundredth.
Answers
A= a^2 (3√3)/2
we replace a with 4
A=41.57
The area of a regular hexagon with a side of 4m is 24√3.
Side of the regular hexagon = 4m
What is a regular hexagon?A Regular hexagon is a polygon with 6 equal sides.
We know that a regular hexagon with a side p comprises 6 equilateral triangles with a side p.
So, the area of a regular hexagon with side p= area of 6 equilateral triangles with side p.
So, the area of a regular hexagon with side p = [tex]6*\frac{\sqrt{3} }{4} p^{2}[/tex]
The area of a regular hexagon with a side of 4m = [tex]6*\frac{\sqrt{3} }{4} 4^{2}[/tex]
The area of a regular hexagon with a side of 4m =24√3.
Therefore, The area of a regular hexagon with a side of 4m is 24√3.
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25 points!
Answer both! please leave explanation!
Answers
sin 27 = 34/x
x = 34/sin27
x = 74.89
2) to find the value of x you'll use the tangent formula
tan 49 = x/55
55(tan49) = x
63.270
What is the volume of a cylinder with base radius 3 and height 8?
Answers
Answer is provided in the image attached.
Final answer:
The volume of a cylinder with a base radius of 3 and a height of 8 is approximately 226.195 cubic units, using the formula V = πr²h.
Explanation:
The volume of a cylinder is calculated using the formula V = πr²h, where π is the constant pi (approximately 3.14159), r is the radius of the cylinder's base, and h is the height of the cylinder. For a cylinder with base radius 3 and height 8, we use the values directly in the formula:
V = π×(3²)×8
V = π×9×8
V = π×72
V = 3.14159×72
V ≈ 226.195 cubic units
Therefore, the volume of the cylinder is approximately 226.195 cubic units.
I need help math Brainliest
Answers
that is the reason you would want a larger than normal financial reserve
Help: Scientists think the _____ is a solid iron with a layer of liquid iron surrounding it.
1. Outer core
2. Inner core
3. Mantle
4. Crust,
Answers
This figure shows circle Z with chords AB and RS .
mAR=55°
mRB=66°
AB=8 m
RS=8 m
What is mRS ?
Enter your answer in the box
Answers
Answer:
121 degrees
Step-by-step explanation:
I took the test peeps
This is really confusing... making my head hurt. I don't understand it AT ALL. If I get this one wrong, and all the other three like this, I'm gonna fail my test.
Can you figure out number 8 please and show how you got it?
Answers
You're working with a geometric problem where the probability of success is constant in each trial. This is related to the situation where you repeatedly ask students if they live within a five-mile radius. The problems you've mentioned seem to involve figuring out specifics related to degrees and interpreting figures.
Explanation:It sounds like you're dealing with a geometric problem. Geometric problems often involve situations where the probability of success or failure stays constant across trials. For example, you inquire if a person lives within five miles of you - the probability is fixed, regardless of the number of people you ask.
Let's decipher it step by step. Firstly, visualize each instance (trial) as the asking of a question to a student and consider success as the event where the student lives within five miles. Probability of success then stays the same every time you ask.
In problem 91, it's important to understand the degrees involved. The first part mentions 88.6°. Without the full problem, it's hard to give a direct answer here, but angles often play a part in geometry and trigonometry problems, it could be related to that. As for the figures mentioned (Car X, the hash marks) they would likely be visible on a diagram accompanying your problem and would inform the solution.
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Suppose that x=6 and y=8. If y is inversely related to x, what it y when x=3?
4
5
16
18
Answers
Credit to: Jdoe0001.
C. 16
Colinda has just purchased her first home for $125,000. She put down a 20 percent down payment of $25,000 and took out a 4 percent mortgage for the rest. Her mortgage payment is $477 per month. How much of her first monthly mortgage payment is amortization?
Answers
Colinda's first monthly mortgage payment includes $143.70 towards amortization, after subtracting the first month's interest of $333.30 from the total payment of $477.
Explanation:To determine how much of Colinda’s first monthly mortgage payment is for amortization, we must first calculate the amount of her payment that goes towards interest and then subtract this from the total monthly payment.
Colinda bought a house for $125,000, made a 20% down payment ($25,000), and took out a mortgage for the remaining $100,000 at a 4% annual interest rate. Her monthly mortgage payment is $477.
First, calculate the monthly interest rate: 4% annually means 0.04 / 12 per month = 0.003333. Therefore, the first month’s interest on the mortgage is $100,000 * 0.003333 = $333.30.
Next, subtract the interest from the total monthly payment to find the amortization portion: $477 (total monthly payment) – $333.30 (interest) = $143.70 towards amortization.
The amount of Colinda's first monthly mortgage payment that is amortization is approximately $143.67.
To separate the interest portion from the total payment.
First, let's calculate the monthly interest rate:
[tex]\text{Monthly interest rate} = \frac{4 \%}{12} = \frac{0.04}{12} = 0.00333 \text{ (approx.)}[/tex]
Next, we calculate the interest portion of the first payment:
[tex]\text{Interest portion} = \text{Principal} \times \text{Monthly interest rate}[/tex]
[tex]\text{Interest portion} = 100,000 \times 0.00333 = 333.33 \text{ (approx.)}[/tex]
Now, to find the amortization portion, we subtract the interest portion from the total monthly payment:
[tex]\text{Amortization portion} = \text{Total monthly payment} - \text{Interest portion}[/tex]
[tex]\text{Amortization portion} = 477 - 333.33 = 143.67[/tex]
what is the answer too......5(x+9)
Answers
To solve for x in this problem, we need to distribute the 5 using the distributive property and then simplify.
5 * x + 5 * 9
= 5x + 45
So, the most simplified form of this expression would be 5x + 45.
Hope this helps!
5*x + 5*9 =
5x + 45
You have to get the x alone so divide both of them by 5
5x/5 + 45/5 =
x + 9
To get the x alone subtract it.
x - x + 9 =
9 = -x can't leave x a negative so dived both sides by -1
9/-1 = -x/-1 =
-9 = x or x = -9
Hope this Helps!
Identify the 25th term of the arithmetic sequence 2, 1 and 3 over 5,
1 and 1 over 5 …
@ranga
Answers
1 and 3/5 = (5+3)/5 = 8/5
1 and 1/5 = (5+1)/5 = 6/5
Therefore your arithmetic sequence is 2, 8/5, 6/5, ...
In an arithmetic sequence, the difference between a given term and the preceding one is equal to the difference between the following term and the given one. In your case:
d = 8/5 - 2 = (8-10)/5 = -2/5
As a prove: d = 6/5 - 8/5 = -2/5
Now, in order to find the 25th term you need to apply the formula:
an = a + (n - 1)d
where an is the number you are looking for, a is the first term, n is the term you are looking for and d is the distance.
Hence,
a₂₅ = 2 + (25-1)(-2/5) = 2 - 24·2/5 = 2 - 48/5 = (10-48)/5 = -38/5
-7 3/5 is the correct answer simplified.
Find the number of sides of a regular polygon if the interior angle is 150
Answers
360/30= 12.
remember that no matter what is the polygon the sum of EXTERIOR angle is 360.
and 1 exterior angle + 1 interior angle = 180.
What was the original price if:
a
after increasing by 30% it became $520?
Answers
130% x = 520 Change a % to a decimal
(130/100) x = 520
1.3 x = 520 Divide by 1.3
x =520 / 1.3
x = 400
So the original cost of the item was 400 dollars.
Answer:
Original price was $400.
Step-by-step explanation:
Let the original price = x dollars.
It is given that the new price is obtained by increasing the original price by 30% i.e. 0.3
As, the new price is $520.
So, we have the relation,
[tex]x+0.03x=520[/tex]
i.e. [tex]1.3x=520[/tex]
i.e. [tex]x=\frac{520}{1.3}[/tex]
i.e. x = 400
Hence, the original price was $400.
the leg of each isosceles right triangle when the hypotenuse is of the given measure. Given = 5sqrt6
Answers
hey I really need help its a test -3x=48
5x-1=29
4(x-6)+7=23
3(x-4)+5x=4
Answers
5x-1=29 --> x=6
4(x-6)+7=23 --> x=10
3(x-4)+5x=4 --> x=2
The focal length, F, in a camera is given by the following function, where d is the distance from the lens in the camera to the object being photographed.
F = 2.24d/ d +2.24
Write an equation that expresses distance, d, as a function of the focal length, F.
Answers
[tex]F= \frac{2.24d}{d+2.24} [/tex]
[tex]F(d+2.24)=2.24d[/tex]
[tex]Fd+2.24F=2.24d[/tex]
Next factor out d to obtain
[tex]2.24F=d(2.24-F)[/tex]
[tex]d= \frac{2.24F}{2.24-F} [/tex]
Using function notation: [tex]G(d)= \frac{2.24F}{2.24-F} [/tex]
Answer: D) d = -2.24F/F-2.24
A certain drug is made from only two ingredients: compound a and compound
b. there are 7 milliliters of compound a used for every 4 milliliters of compound
b. if a chemist wants to make 748 milliliters of the drug, how many milliliters of compound b are needed?
Answers
Medal will be given to the best answer.
Which of the following is a solution to the equation y = 3x - 1 ?
A. (4,1)
B. (2,5)
C. (4,3)
D. (0, -3)
Answers
For this problem, simply plug in the X values and calculate the Y value and verify that the Y value matches the value given.
A. (4,1); X = 4: 3x - 1 = 3*4 - 1 = 12 - 1 = 11. 11 does not match 1.
B. (2,5); X = 2: 3x - 1 = 3*2 - 1 = 6 - 1 = 5. 5 matches 5.
C. (4,3); X = 4: 3x - 1 = 3*4 - 1 = 12 - 1 = 11 does not match 3
D. (0,-3); X = 0: 3x - 1 = 3*0 - 1 = 0 - 1 = -1 does not match -3
And of the above, only option "B. (2,5)" matches.
Look at the figures. How can you prove these triangles are congruent?
∆ABC ≅ ∆DEF by the SAS Postulate.
∆ABC ≅ ∆DEF by the SSS Postulate.
It is not possible to determine if the triangles are congruent.
Answers
by SSS, you need to know AC=DF, but there is no way to know it.
by SAS, you need to know ∠ABC=∠DEF, no way to know as well.